A statistical approach for array CGH data analysis

BACKGROUND: Microarray-CGH experiments are used to detect and map chromosomal imbalances, by hybridizing targets of genomic DNA from a test and a reference sample to sequences immobilized on a slide. These probes are genomic DNA sequences (BACs) that are mapped on the genome. The signal has a spatial coherence that can be handled by specific statistical tools. Segmentation methods seem to be a natural framework for this purpose. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose BACs share the same relative copy number on average. We model a CGH profile by a random Gaussian process whose distribution parameters are affected by abrupt changes at unknown coordinates. Two major problems arise : to determine which parameters are affected by the abrupt changes (the mean and the variance, or the mean only), and the selection of the number of segments in the profile. RESULTS: We demonstrate that existing methods for estimating the number of segments are not well adapted in the case of array CGH data, and we propose an adaptive criterion that detects previously mapped chromosomal aberrations. The performances of this method are discussed based on simulations and publicly available data sets. Then we discuss the choice of modeling for array CGH data and show that the model with a homogeneous variance is adapted to this context. CONCLUSIONS: Array CGH data analysis is an emerging field that needs appropriate statistical tools. Process segmentation and model selection provide a theoretical framework that allows precise biological interpretations. Adaptive methods for model selection give promising results concerning the estimation of the number of altered regions on the genome

An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal

The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging from ecology to medicine involve large collections of individuals, and a further intellectual challenge is to model population-level behavior based on a detailed individual-level model. Because of the large number of interacting individuals and because the individual-level model is complex, classical direct Monte Carlo simulations can be very slow, and often of little practical use. In this case, an equation-free approach may provide effective methods for the analysis and simulation of individual-based models. In this paper we analyze equation-free coarse projective integration. For analytical purposes, we start with known partial differential equations describing biological random walks and we study the projective integration of these equations. In particular, we illustrate how to accelerate explicit numerical methods for solving these equations. Then we present illustrative kinetic Monte Carlo simulations of these random walks and show a decrease in computational time by as much as a factor of a thousand can be obtained by exploiting the ideas developed by analysis of the closed form PDEs. The illustrative biological example here is chemotaxis, but it could be any random walker which biases its movement in response to environmental cues.Comment: 30 pages, submitted to Physica

The group fused Lasso for multiple change-point detection

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are proposed to solve the resulting optimization problems, either exactly or approximately. Conditions are given for consistency of both algorithms as the number of signals increases, and empirical evidence is provided to support the results on simulated and array comparative genomic hybridization data

Automated smoother for the numerical decoupling of dynamics models

<p>Abstract</p> <p>Background</p> <p>Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure.</p> <p>Results</p> <p>In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from <it>in-vivo </it>NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations.</p> <p>Conclusion</p> <p>The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.</p

Autonomous Identification and Tracking of Thermoclines

All data acquired from oceanic water features is hard and crucial work. It's hard due to the difficulty to obtain the same data given the unfavourable conditions.It requires, therefore, equipment that are reliable in the measurements of the desired characteristics and robust equipment, that is to say, equipment that are capable to withstand unfavorable and variable conditions in spatial and temporal terms. Due to these same spatial and temporal changes, the traditional methods do not prove to be the most adequate, because these methods do not have sufficient capacity to sample measurements of the dynamic characteristics of oceanographic processes.Thus, to obtain such measurements the use of the autonomous robotic systems proves to be important. With these systems, it is ensured a faster, more efficient and systematic sampling and is not subject to human error. The data acquisition is then a crucial work to understand how oceanographic process happens and varies in time and space. This work proposes an implementation of an algorithm to perform the tracking of the thermocline, from the stratification model of the oceanic water.This model is a parametric model. This work will also take into account the capacity to perform measurements with a sampling capable of adapting the depth control of the underwater vehicle.The stratification of the oceanic water happens when exists different features between different layers. One of these layers is the thermocline. At this layer, the water temperature decreases rapidly with increasing depth. The characterization of the thermocline is so important to marine biology, given the high concentration of phytoplankton in this level, as for acoustic communications equipments or military services, given the special characteristics of speed sound in this level.The model of this stratification will be used to aid in the thermocline's tracking process. This model will serve as a basis for the algorithm to adapt the control in order to carry out the tracking with the greatest success, in real time. This algorithm will focus on the variations in the vertical temperature gradient.The algorithm responsible detect and track of the thermocline will be run on a profiler. The profiler is a vehicle that moves along the vertical axis. However, when subject to tides, the natural process in aquatic environments drifts along the horizontal axis. A set of sensors capable of measuring the water temperature and the depth at which the vehicle is below water shall be placed in this vehicle. These sensors will be important to calculate the vertical gradient

Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table

Determination of Soybean Oil, Protein and Amino Acid Residues in Soybean Seeds by High Resolution Nuclear Magnetic Resonance (NMRS) and Near Infrared (NIRS)

A detailed account is presented of our high resolution nuclear magnetic resonance (HR-NMR) and near infrared (NIR) calibration models, methodologies and validation procedures, together with a large number of composition analyses for soybean seeds. NIR calibrations were developed based on both HR-NMR and analytical chemistry reference data for oil and twelve amino acid residues in mature soybeans and soybean embryos. This is our first report of HR-NMR determinations of amino acid profiles of proteins from whole soybean seeds, without protein extraction from the seed. It was found that the best results for both oil and protein calibrations were obtained with a Partial Least Squares Regression (PLS-1) analysis of our extensive NIR spectral data, acquired with either a DA7000 Dual Diode Array (Si and InGaAs detectors) instrument or with several Fourier Transform NIR (FT-NIR) spectrometers equipped with an integrating sphere/InGaAs detector accessory. In order to extend the bulk soybean samples calibration models to the analysis of single soybean seeds, we have analized in detail the component NIR spectra of all major soybean constituents through spectral deconvolutions for bulk, single and powdered soybean seeds. Baseline variations and light scattering effects in the NIR spectra were corrected, respectively, by calculating the first-order derivatives of the spectra and the Multiplicative Scattering Correction (MSC). The single soybean seed NIR spectra are broadly similar to those of bulk whole soybeans, with the exception of minor peaks in single soybean NIR spectra in the region from 950 to 1,000 nm. Based on previous experience with bulk soybean NIR calibrations, the PLS-1 calibration model was selected for protein, oil and moisture calibrations that we developed for single soybean seed analysis. In order to improve the reliability and robustness of our calibrations with the PLS-1 model we employed standard samples with a wide range of soybean constituent compositions: from 34% to 55% for protein, from 11% to 22% for oil and from 2% to 16% for moisture. Such calibrations are characterized by low standard errors and high degrees of correlation for all major soybean constituents. Morever, we obtained highly resolved NIR chemical images for selected regions of mature soybean embryos that allow for the quantitation of oil and protein components. Recent developments in high-resolution FT-NIR microspectroscopy extend the NIR sensitivity range to the picogram level, with submicron spatial resolution in the component distribution throughout intact soybean seeds and embryos. Such developments are potentially important for biotechnology applications that require rapid and ultra- sensitive analyses, such as those concerned with high-content microarrays in Genomics and Proteomics research. Other important applications of FT-NIR microspectroscopy are envisaged in biomedical research aimed at cancer prevention, the early detection of tumors by NIR-fluorescence, and identification of single cancer cells, or single virus particles in vivo by super-resolution microscopy/ microspectroscopy